Model Comparison Worksheets Grade 11

1. Emma is analyzing the growth of three different functions over time. On a coordinate grid, she plots the graphs of y = 5x, y = 5x², and y = 5(2^x) for x ≥ 0. For x = 0, all three functions start at (0,0) or (0,5). Looking at the graphs, which function will eventually have the greatest y-value for very large values of x, and which will have the smallest? Explain how the shapes of the graphs compare.
2. Compare f(x) = 9x + 14, g(x) = x^2 + 11, and h(x) = 4^x for large x. Which function grows fastest?
3. Aroha is comparing three functions: f(x) = 9x + 11, g(x) = 3x² + 5, and h(x) = 7^x. For large x, which function grows fastest?

…and 4 more problems

1. Compare f(x)=11x+15, g(x)=x²+13, h(x)=4^x for large x. Which function grows fastest?
2. Compare f(x) = 7x + 12, g(x) = 2x² + 7, and h(x) = 7^x for large x. Which function grows fastest?
3. Sophia is an environmental scientist studying the growth of three different algae species in a lake. Species L grows linearly: its population (in thousands) is modeled by L(t) = 21 + 6t, where t is the number of weeks after initial observation. Species Q grows quadratically: Q(t) = 0.5t² + 21. Species E grows exponentially: E(t) = 21(1.26)^t. Sophia wants to know which species will have the largest population after 6 weeks. Determine the population of each species at t = 6 and identify which model predicts the highest population.

…and 5 more problems

1. Aroha is comparing three functions: f(x) = 9x + 14, g(x) = 2x² + 11, and h(x) = 4^x. For large values of x, which function grows fastest?
2. The graphs of three functions are drawn on the same coordinate plane: f(x) = 5x + 10, g(x) = x^2 + 5, and h(x) = 5(2^x). For x ≥ 0, which function will eventually have the greatest y-value as x increases without bound, and at what approximate x-value does the exponential function overtake the quadratic function? (Use integer or fractional approximations.)
3. Charlotte is an environmental scientist studying three different models for the spread of an invasive plant species in a national park. The area covered by the species (in square meters) is predicted by three models, where t represents the number of years since the species was first detected. Model L (linear): A(t) = 850 + 90t. Model Q (quadratic): A(t) = 7t² + 850. Model E (exponential): A(t) = 850(1.12)^t. After 12 years, which model predicts the largest area covered by the invasive species?

…and 3 more problems